Science has taught us that we're usually not special
Maybe, but due to anthropic effects, this is one of the times in which we definitely cannot use the we're-not-special rule of thumb. Noting that we happen to have developed gives us absolutely no evidence about the rarity of observers that can notice that they've developed (except that it rules out theories that make it so rare that even 1 observer is unlikely).
if the probability of intelligent life developing in a 3 billion year period is 1/50 we might just need to wait a couple more billion years for the next group
Without more information about The Great Filter, most of the probability density does not reside in such perfectly balanced orders of magnitude (like 2% per 3Gyr-galaxy) to make us happen to be first. Though it's an open possibility that we're the first but not the only life that will develop, it's extremely unlikely that two huge numbers that could conceivably be orders of magnitude apart, happen to line up so closely.
I'm not sure I follow your last paragraph. What are the two huge numbers in this context?
One serious issue for evaluating existential risk is working out whether most of the Great Filter is behind us or in front of us. This relates to the Drake Equation and similar attempts to estimate the frequency of life in an obvious way.
Over the last few years, it has become increasingly apparent that extrasolar planets are common. However, what fraction of these planets lie in their stars habitable zone has still been an open question, primarily because most of our current methods for planet finding easily find planets that are either very large or are very close to their star (ideally both).
A new study, using the data from the Kepler spacecraft, estimates that about a third of all stars similar to the sun have at least one planet in the habitable zone. There are some issues with this estimate, and Phil Plait discusses them at his blog. The estimate has a large amount of variance. The paper actually estimates 34% +/- 14% and the issues that Phil brings up increases the uncertainty in both directions but it seems safe at this point to consider this not being very far off.
One obvious issue from a Fermi perspective is that some systems will likely have multiple planets in this zone. Also, having planets in the habitable zone is clearly not sufficient for life. By the standard estimates for habitable zones, Venus and Mars are both in the habitable zone of the sun. And there may very well be ways for life to arise outside the habitable zone. Moons like Europa and Titan seem to be excellent candidates, and we can't rule out more exotic forms of life in other habitats although that seems not too likely right now.
However, one thing this makes clear: The part of the Great Filter that is behind us that is due to planets not lying inside the habitable zone is small. So the question is, what does this mean for our estimates of how much of the Filter is behind us and how much is in front of us?